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continuity of length function $l: T(X) \times MF \to \mathbb R$

.$ The question is, is there a basic and convenient way to see the continuity of this function $l$. Here $T(X)$ is given the usual topology and $MF$ the topology of intersection numbers. … .$ A same question is, is there a basic and convenient way to see the continuity of this function $L$. …
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